Landau's Problem of Degenerate Plasma Oscillations in Slab with Specular Boundary Conditions

TL;DR

This paper analytically solves the problem of plasma oscillations in a slab with specular boundary conditions, deriving explicit formulas for electron distribution, electric field, and energy absorption.

Contribution

It provides a novel analytical solution for plasma oscillations in slabs with specular boundary conditions, including spectrum coefficients and energy absorption calculations.

Findings

Explicit formulas for electron distribution at the boundary

Analytical expressions for electric field in the slab

Calculated energy absorption of the electric field

Abstract

In the present paper the linearized problem of plasma oscillations in slab (particularly, thin films) in external longitudinal alternating electric field is solved analytically. Specular boundary conditions of electron reflection from the plasma boundary are considered. Coefficients of continuous and discrete spectra of the problem are found, and electron distribution function on the plasma boundary and electric field are expressed in explicit form. Absorption of energy of electric field in slab is calculated.